$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 6x + 8$ and $ JT = 2x + 44$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {6x + 8} = {2x + 44}$ Solve for $x$ $ 4x = 36$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 6({9}) + 8$ $ JT = 2({9}) + 44$ $ CJ = 54 + 8$ $ JT = 18 + 44$ $ CJ = 62$ $ JT = 62$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {62} + {62}$ $ CT = 124$